Isothermal Flow

What is the fundamental assumption for the model of isothermal flow described in the chapter?

In the momentum equation for isothermal flow, -AdP - τ_w * d(A_wetted area) = m_dot * dU, what does the term τ_w represent?

How is the hydraulic diameter, DH, defined in the context of isothermal flow?

What is the relationship between the Fanning friction factor (f), shear stress (τ_w), density (ρ), and velocity (U)?

What is the limiting Mach number for isothermal flow from a mathematical point of view, beyond which the right-hand side of the integrated friction equation becomes negative?

In an isothermal flow, what happens to the stagnation temperature as the flow progresses?

In the derivation for the dimensionless representation of isothermal flow, what is the relationship between the fractional change in pressure (dP/P) and the fractional change in velocity (dU/U)?

For a tube with a Fanning friction factor f = 0.005, a length L = 5000 m, and a diameter D = 0.25 m, what is the value of the dimensionless resistance term 4fL/D?

For an isothermal flow, how is the pressure ratio P/P_star related to the Mach number M and the specific heat ratio k?

What is the relationship for the velocity ratio U/U_star in a choked isothermal flow as a function of Mach number (M) and specific heat ratio (k)?

For which of the following scenarios is the isothermal flow model most applicable?

When expanding the solution for isothermal flow for a small pressure drop, what does the expression 4fL/D approximate to in terms of the pressure drop ratio χ and initial Mach number M1?

Why does the core assumption of the isothermal flow model break down for the supersonic branch?

A typical value for the Fanning friction coefficient is f = 0.005. For a case where the dimensionless friction term 4fL_max/D is 10, what is the value of L_max/D?

According to the relationship dP/P = -[kM^2 / (2 * (1 - kM^2))] * (4f dx/D), what happens to the pressure (P) in a subsonic isothermal flow where M < 1/sqrt(k)?

According to the relationship dP/P = -[kM^2 / (2 * (1 - kM^2))] * (4f dx/D), what is the behavior of pressure (P) in a supersonic isothermal flow where M > 1/sqrt(k)?

The integration of the separated variables for dimensionless friction from an initial Mach number M to the choking point yields the maximum resistance 4fL_max/D. What is this integrated expression?

For incompressible flow, the pressure loss P1 - P2 is given by (4fL/D) * (ρ * U^2 / 2). How is this different from the isothermal flow model?

Which equation represents the energy equation for isothermal flow through a control volume where heat transfer occurs?

What is the expression for the stagnation temperature ratio T0/T0_star in an isothermal flow?

Given a specific heat ratio k=1.4, if the dimensionless resistance 4fL/D for an isothermal flow is 13.9747, what is the corresponding Mach number M?

For an isothermal flow with a Mach number of 0.5 and a specific heat ratio of k=1.4, what is the pressure ratio P/P_star?

For an isothermal flow with a Mach number of 0.8 and a specific heat ratio of k=1.4, what is the stagnation temperature ratio T0/T0_star?

For isothermal flow, what does the differentiation of the mass conservation equation yield in dimensionless form?

As a subsonic isothermal flow (M < 1/sqrt(k)) moves down a pipe with friction, what happens to the Mach number?

In a subsonic isothermal flow, what happens to the stagnation pressure P0?

As a subsonic isothermal flow moves down a pipe, how does the fluid density (ρ) change?

The equation 4fL/D = 2 ln(M1) - 1 - (1 - kM2^2)/(kM2^2) is a reduced approximation for a specific scenario. What is this scenario?

The stagnation pressure ratio P0/P0_star can be expressed as a function of the static pressure ratio P/P_star and Mach number M. What is this expression?

For a large entrance length (large 4fL/D), what is the approximate relationship for the entrance Mach number M1?